Messages
Last message this time: I have put proposed solutions of the exam problems on the web!
Geir
The exact curriculum:
- Chapter 1
- Chapter 2: From the start on page 17 until "Tensor products of modules" on page 24
- Chapter 3, Chapter 4
- Chapter 5: From the start on page 59 to page 63 including prop.5.13. In addition prop 5.18. on page 65.
- Chapter 6, Chapter 7, Chapter 8
- Chapter 9: From the start on page 93 until "Fractional Ideals" on page 96
- Chapter 10: From "Filtrations" on page 105 until Corollary 10.10. on page 107
- Chapter 11: Page 116 until "Regular local rings" on page 123
Geir
Today's lecture will be the last with new theory. Next week I plan to do some problems from older exams and some repetition. If there are parts of the curriculum or problems that you want me to speak about, please tell me.
I do not plan any activity on on Wednesday 7. December, but I will be room and answere question - sort of last day first aid.
The old exams I plan to do are:
Wednesday 10. December 2008 No 1 b) and c)
Wednesady 9. December 2009
Friday 10. December 2010 , except No 1 alternative 1.
You find them on the web under the link "Oppgaver". For the moment there are only norwegian versions, but I am working on it, and will pretty soon post translations.
Solutions for Ark5 are also under way.
Geir
I have finished correcting the assignment, and everybody passed! You find your assignment at 7. floor in Niels Henrik Abels Hus (Mattebygget).
I have put a solution on the web. Remember that thing often can be done and written in different ways, so this is the way I propose to do it.
And of course, as usual, any question or comment is welcome.
Geir
NB: There is no lecture on wednesday december 16.
On friday december 17., we will do theory instead of exercises. Solutions for Ark4 are now on the net. Of course, as usual, any question is welcome.
Last friday we finished chapter 9. The paragraph called "Fractional ideals" is not part of the curriculum. In chapter 10 I will only do what is needed for chapter 11. This means the part of the paragraph called "Filtrations" starting on page 105 and ending with corollary 10.10 on page 107.
Geir
Yesterday we had the great Hilbert day! We proved Hilbert's basis theorem and Hilbert's Nullstellensatz. I spoke a lot about the Nullstellensatz not following the book all the time (but did everything in the book).
To morrow we continue with primary decompositions in noetherian rings and I guess we will also have time for the chapter on Artin rings (at least we start on it).
Geir
About the madatory assignment There is a misprint in problem 4. New version on the web. Sorry - Geir
NB: A new version of Ark4 on the web. A correction of one of the exercises and a few more.
Geir
Proposed solutions for Ark2 is now on the web.
Geir
On friday we finish chapter 5 and started on chapter 6 - mostly with examples. We will take up chapter 5 on wedensady.
Yesterday I did the first paragraph in chapter 5, called Integral Dependence. To morrow I'll do the going up theorem. I'll state the going down theorem, but not give the proof. And for the moment we skip the whole paragraph called Valuation Rings (may be we need a small part of it later, but in case, we do it then.)
What we skip is of course not part of the curriculum.
Geir
I have written down solutions to the exercises on Ark1. Things can be done in , so these are proposed way of solving the problems.
I'll try to follow with the other exercises, if I get time. You must try your self (!!), so a certain delay between the exercises an the solutions is a good thing.
Geir
Mandatory assignment: The assignment is now placed on the net (a few days before schedule which gives you some more time). The deadline is Thursday November 3 at 16.00.
Geir
Some of you have asked for supplementary texts. You can try the link
http://www.jmilne.org/math/xnotes/CA.pdf
containing notes by J. Milne. At least part of it might be useful.
Take also a look at notes by Ash:
http://www.math.uiuc.edu/~r-ash/ComAlg.html
Geir
Last wednesday we stared on chapter 4 about primary decomposition and arrived at theorem 4.5. We go from there (but with a serious recapitulation) to morrow, and hopefully we will have time to come through chapter 4.
Only exercises on friday - I'll do those on Ark2.
Geir
I have put a new sheet of exercises on the homepage.
Geir
Important : No lecture next friday!
Geir
To day I finished chapter 3. I defined localisation for modules and did the paragraph called local properties. Next week is devoted to chapter 4 - primary decomposition - this means wednesday as I have to cancel the lecture on friday.
I also think we have too little time for exercises - so from no on we will devote every second friday entirely (i.e., both hours) to exercises.
Geir
Yesterday – wednesday September 14 – I did what was left of the paragraph on Nakayama's lemma and the paragraph on exact sequences.
Friday I'll do tensor products
Geir
New sheet of exercises out on the web.
Geir